The present study deals with the reflection of SV-waves at a free surface in the presence of magnetic field, initial stress, voids and gravity. When an SV-wave incident on the free surface of an elastic half space, two damped P-waves and an SV-wave are reflected. Among these waves, P-waves are only affected by magnetic fields whereas SV-waves are influenced by both, initial stress and magnetic fields. Effect of gravity is negligible whereas voids played a significant role. These observations can be helpful for seismology and earthquake sciences.

This work investigates rotational effects on propagation and reflection of waves at the free surface of a micropolar fibre-reinforced medium with voids under magnetic fields. When the P-wave is incident on the free surface, there exist four coupled reflected plane waves traveling in the medium; quasi-longitudinal displacement (qLD) wave, quasi-transverse displacement (qTD) wave, quasi-transverse microrotational (qTM) wave and a wave due to voids. Normal mode analysis is adopted in concomitant with Snell's laws, and appropriate boundary conditions in determination of the solution. Amplitude ratios which correspond to reflected waves in vertical and horizontal components are presented analytically and graphically.

The present investigation envisages on the Mathematical modeling of waves propagating in a porous micropolar fibre-reinforced structure in a half-space and liquid interface. The harmonic method of wave analysis is utilized, such that, the reflection and transmission of waves in the media were modelled and it’s equations of motion analytically derived. It was deduced that incident longitudinal wave in the solid structure yielded four reflected waves given as; quasi–P wave (qLD), quasi–SV wave, quasi–transverse microrotational (qTM) wave and a wave due to voids and one transmitted wave known as the quasi-longitudinal transmitted (qLT) wave. The phase velocity in the liquid medium is independent of angle of propagation as observed. The corresponding amplitude ratios of propagations for both reflected and transmitted waves are analytically derived by employing Snell’s law. The model would prove to be of relevance in the understanding of modeling of the behavior of propagation phenomena of waves in micropolar fibre-reinforecd machination systems resulting in solid/liquid interfaces especially in earth sciences and in particular seismology, amongst others.

This article is concerned with the investigation of reflection of waves at the free surface of a rotating micropolar fibre-reinforced thermoelastic medium, in the presence of a magnetic field using Green and Lindsay theory. It is observed that when a P-wave is incident on the free surface of rotating micropolar fibre-reinforced thermoelastic medium in the presence of a magnetic field, four waves are reflected; quasi-longitudinal displacement (qLD), quasi-transverse displacement (qTD), quasi-transverse micro-rotational (qTM) and quasi-thermal waves. The normal modes method, also called the harmonic solution approach, is used simultaneously with Snell's laws and Maxwell's equation, governing electromagnetic fields, in the determination of a solution for the micropolar fibre-reinforced modelled problem. Amplitude ratios or reflection coefficients, which correspond to reflected waves in vertical and horizontal components, are presented analytically. Moreover, the reflection coefficients are presented using numerically simulated results in graphical form for a particular chosen material. We observe that the micropolar fibre-reinforced, rotation, and magneto-thermoelastic field parameters, have varied degree of effects on the propagation and reflection of waves in the medium. The study should be helpful in understanding the behaviour of propagation and reflection of rotating micropolar fibre-reinforced magneto-thermoelastic machination fields and on future works about behaviour of seismic waves.

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